Question

One number is three times another number. If 15 is added to both the numbers, then one of the new numbers becomes twice that of the other new number. The numbers are?

Answer 1

Hint: The given question is an example of a word problem in which we are given relations amongst the numbers and forming the equation according to the relation we will be able to find the two numbers.

Complete step-by-step solution:
According to the given question we are having two numbers and also both the numbers are related by relations given in the question.
Let one number be x and then we are given that second number is three times the first number
That means the second number is 3x.
Now, we are asked to add 15 to both the numbers.
Therefore, the new numbers are $x+15$ and $3x+15$ .
Now, one of the new numbers is twice another new number and since we know that $x+15$is smaller than another number therefore, $3x+15=2\left( x+15 \right)$
Now, simplifying this we get,
 $\begin{align}
  & 3x+15=2\left( x+15 \right) \\
 & \Rightarrow 3x+15=2x+30 \\
 & \Rightarrow x=15 \\
\end{align}$
Therefore, one number is 15 and we know another number was thrice the first number, therefore, another number is 45.
Hence, the two numbers are 15 and 45.

Note: These types of questions are mainly asked in the competitive examinations in which we need to do fast calculation so for that we need to interpret the questions easily and then find the numbers and also, we need to form equations and solve with the simplest method we can and which involves less chances of calculation mistakes.